109 lines
3.1 KiB
Markdown
109 lines
3.1 KiB
Markdown
---
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title: "Partial differential"
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chunk: 1/1
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source: "https://en.wikipedia.org/wiki/Partial_differential"
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category: "reference"
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tags: "science, encyclopedia"
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date_saved: "2026-05-05T07:22:50.785154+00:00"
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instance: "kb-cron"
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---
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The character ∂ (Unicode: U+2202) is a stylized cursive d mainly used as a mathematical symbol, usually to denote a partial derivative such as
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∂
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z
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/
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∂
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x
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{\displaystyle {\partial z}/{\partial x}}
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(read as "the partial derivative of z with respect to x"). It is also used for boundary of a set, the boundary operator in a chain complex, and the conjugate of the Dolbeault operator on smooth differential forms over a complex manifold.
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It should be distinguished from other similar-looking symbols such as lowercase Greek letter delta (δ) or the lowercase Latin letter eth (ð).
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== History ==
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The symbol was introduced originally in 1770 by Nicolas de Condorcet, who used it for a partial differential, and adopted for the partial derivative by Adrien-Marie Legendre in 1786.
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It represents a specialized cursive type of the letter d, just as the integral sign originates as a specialized type of a long s (first used in print by Leibniz in 1686).
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Use of the symbol was discontinued by Legendre, but it was taken up again by Carl Gustav Jacob Jacobi in 1841, whose usage became widely adopted.
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== Names and coding ==
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The symbol is variously referred to as "partial", "curly d" or "Jacobi's delta", or as "del" (but this name is also used for the "nabla" symbol ∇). It may also be pronounced simply "dee", "partial dee", "doh", "dow" or "die".
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The Unicode character U+2202 ∂ PARTIAL DIFFERENTIAL is accessed by HTML entities ∂ or ∂, and the equivalent LaTeX symbol (Computer Modern glyph:
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∂
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{\displaystyle \partial }
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) is accessed by \partial.
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== Uses ==
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∂ is also used to denote the following:
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The Jacobian
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∂
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(
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x
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,
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y
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,
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z
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)
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∂
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(
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u
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,
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v
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,
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w
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)
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{\displaystyle {\frac {\partial (x,y,z)}{\partial (u,v,w)}}}
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.
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The boundary of a set in topology.
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The boundary operator on a chain complex in homological algebra.
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The boundary operator of a differential graded algebra.
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The conjugate of the Dolbeault operator on complex differential forms.
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The boundary ∂(S) of a set of vertices S in a graph is the set of edges leaving S, which defines a cut.
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== See also ==
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d'Alembert operator
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Differentiable programming
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Differential operator § Notations
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List of mathematical symbols
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Notation for differentiation
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𝒹 (Unicode MATHEMATICAL SCRIPT SMALL D)
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ꝺ (lowercase d in Insular script)
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δ (lowercase Greek Delta)
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д (lowercase Cyrillic De, looks similar when italicized in some typefaces)
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== References == |